There seems to be an implication that Google somehow obtained this information and added it to her account automatically, while this might be technically feasible I'm not aware of any actual claim that this is the case.
Much more likely is that the user entered her real name when she signed up initially and just forgot about it (how many people here can recall what details they gave to MySpace or Yahoo a decade ago?)
That's still missing the point. Even IF the user gave that information voluntarily in the past (she claims she didn't and we should believe her by default in my world, out of courtesy and respect) - the quote continues and says that there wasn't a setting to be found that referred to the wrong/unwanted name.
IF that name was given previously the user still needs to have final say about her appearance online, her very own account data. Saying "You probably gave it out earlier and yeah, maybe there's no way to remove it from the history of your account" wouldn't make Google look better in any way.
No she doesn't. The exact quote is "I don't remember" which is completely different from "I didn't". That's the danger of implication, it makes you think one thing is meant while another is actually said.